There are ways other than / in addition to handlebar input to balance gravity including but not limited body positioning, throttle opening and arc of turn.

Stand beside your bike, left hand on the left grip, right hand on the grab rail and move the bike forward while maintaining full left lock.
No homework or questions to answer just make your own obsevations.

I'm not a big fan of Tony Foale's explainations.
Link is to the a diagram only just in case you've never seen the experiment.

Many staunch countersteering sceptics who have held the wheel have an epiphany.
Sometimes you can actually see the penny dropping by the expression on their faces.
Thing is if you spin the wheel really slowly the forces just are not present.

And so the argument goes round and round - just like the bicycle wheel. The faster you spin it the stronger it gets.
To me those who insist countersteering is the only way to turn a motorcyle are missing out on as much as those who instist countersteering is a myth.

Maybe my question belongs in a different thread away from the zealots and sceptics.

I actually have no questions on the subject. I've been on a motorcycle since I was 3 and I'm now 43. You only said exactly what I said but in a long drawn out explanation. Now you want to throw in the rest of it. I'm talking about STEERING, thought I read that somewhere in the thread title.

Another thing to add.
I have a son who was 10 at the time and had only been on a quad and never on a bicycle. I decided to put him on the tank of the dirt bike and go for a spin. I asked if he wanted to drive and let him go for it. Going very slow he did like he did on the quad and turned into the intended direction. Once he figured out the throttle and got going a bit he leaned to the right but turned to the right as well causing us to go left. Just couldn't wrap his head around it and we spent about a half hour trying, no amount of explanation was going to make it happen. The quad had him brainwashed. I even put my hands over top of his hands so he could feel me push the bar into the intended direction. Not happening. Got him a small bicycle the next day and took the pedals off so he wasn't trying to learn two things at once. While coasting along slow he got it. If he got to the point where that didn't work anymore, the bike went one way and he went the other. That took an hour to fix with no input from me and he was good to go. Back on the tank and we drove around all day. Next week he had a crf50 of his own. Some things you can explain all day with little science experiments and diagrams but really just get somewhere safe and get your head out of the experience. I can't think of one time in my life I had a thought about how I was going to get my bike while on the street or in the dirt where I needed it to go and its because I was too young to remember being taught , if I even was. It's got to be second nature, if it's not please don't play in traffic. Your brain can learn things without explanation and probably most of the motor skills you posses today were learned by doing.

Many staunch countersteering sceptics who have held the wheel have an epiphany.
Sometimes you can actually see the penny dropping by the expression on their faces.
Thing is if you spin the wheel really slowly the forces just are not present.

And so the argument goes round and round - just like the bicycle wheel. The faster you spin it the stronger it gets.
To me those who insist countersteering is the only way to turn a motorcyle are missing out on as much as those who instist countersteering is a myth.

Maybe my question belongs in a different thread away from the zealots and sceptics.

Here's the problem I have with saying gyroscopic procession is what leans a bike.

To start: Every action has an equal and opposite reaction. (we all know newton's third law)

So you spin the front wheel up and it balances itself in a strait line (as shown by gyroscopes spinning while only one side is supported)

You do the tire "trick" in the link you provided, spinning wheel, you turn it left it wants to lean right. Your theory, and one that I've read before on this site, is that the tendency of the spinning wheel lean right when twisted left is actually what is making the bike lean. (In fact some have said that at highway speeds the gyroscopic effect is the main force that leans the bike) So this theory works like this. You turn the bars left, the gyroscopic effect leans it right. You want to stand the bike up, from a lean right, you turn the bars right the gyroscopic effect leans it left. (am I on point?)

My problem with this is newton's third law. I read it to mean this. Back to the spinning wheel held in your hand example. You turn the spinning wheel to the left, the gyroscopic effect cause the wheel to tilt right with an equal amount of force that you applied by twisting.

If that is the case, and I'm not sure it is which is why I'm posting this. If when you turn the wheel to the right, it exerts an equal amount of force to lean, then the same thing is happening to the front wheel on your motorcycle.

You twist the bars to the left, that force is redirected by the wheel to a lean right.
If that leaning force is equal to the twisting force you applied, then an analog would be simply to pick the bike up by the bars while sitting still. With that in mind, the force I have to apply to the bars to pick the bike up from a 30 degree lean while sitting still in my garage is vastly greater than the force I need to pick the bike up from the same degree of lean while rolling down the road.

So my point is, maybe the gyroscopic effect provides some torque to the lean angle of the bike, equal to the force that I applied to the handlebars. But since the force I applied to the bars is no where near sufficient to lift the bike from it's 30 degree lean, I have to surmise that the majority of the torque is provided by the outsteering of the front wheel caused by countersteering.

My other reasoning is that turning the bars causes a moment gyroscopic torque, but that moment ends once I stop turning the bars. But my change in lean angle doesn't stop until I straiten the bars. I turn the bars a split second to the left, but hold that turn for 1/2 a second while the bike transitions from left lean to right lean. What's causing the bike to lean for the majority of that 1/2 second when I'm not actively turning the bars? IMHO it's the ousteering of the wheel, not the gyroscopic effect.

I actually have no questions on the subject. I've been on a motorcycle since I was 3 and I'm now 43. You only said exactly what I said but in a long drawn out explanation. Now you want to throw in the rest of it. I'm talking about STEERING, thought I read that somewhere in the thread title.

Another thing to add.
I have a son who was 10 at the time and had only been on a quad and never on a bicycle. I decided to put him on the tank of the dirt bike and go for a spin. I asked if he wanted to drive and let him go for it. Going very slow he did like he did on the quad and turned into the intended direction. Once he figured out the throttle and got going a bit he leaned to the right but turned to the right as well causing us to go left. Just couldn't wrap his head around it and we spent about a half hour trying, no amount of explanation was going to make it happen. The quad had him brainwashed. I even put my hands over top of his hands so he could feel me push the bar into the intended direction. Not happening. Got him a small bicycle the next day and took the pedals off so he wasn't trying to learn two things at once. While coasting along slow he got it. If he got to the point where that didn't work anymore, the bike went one way and he went the other. That took an hour to fix with no input from me and he was good to go. Back on the tank and we drove around all day. Next week he had a crf50 of his own. Some things you can explain all day with little science experiments and diagrams but really just get somewhere safe and get your head out of the experience. I can't think of one time in my life I had a thought about how I was going to get my bike while on the street or in the dirt where I needed it to go and its because I was too young to remember being taught , if I even was. It's got to be second nature, if it's not please don't play in traffic. Your brain can learn things without explanation and probably most of the motor skills you posses today were learned by doing.

perhaps an inmate would care to try this experiment i just thought up and report back.
rig a steering stop so the bars will not turn past dead straight in one direction. lets say can turn left only.
next put an electronic protractor on the bike to determine true vertical
have a helper hold the bike true vertical while the rider gets moving.
rider attempts left turn
report back with results

It shouldn't be alarming to me that riders still question how to steer their motorcycles but it is. Apparently, even after 90 years when it was first observed by the Wright brothers some confusion remains on this subject . Yes, their first engineering attempts were as bicycle manufacturers. The very observant brothers, determined that tandem-wheeled (one wheel in front of the other) vehicles countersteer. That was and still is correct.

The Solution

Make a bike that has two sets of bars. One set as normal, the other set would be solid-mounted to the frame so they were not connected to and did not rotate the forks. This, as my theory went, would answer the question. And it does.

Dirty Exceptions

Before I go any further I want to address off-road motorcycles. An off-road motorcycle will easily steer by pressing down on the inside peg, and in conjunction with shifting the upper body mass, will go over pretty easily . Still not what I would call good control but it can be done fairly efficiently.
Again, I am not a true tech guy, but it occurs to me that the small contact patch on knobbies or dual sport tires plus dirt bike steering geometry (which is not intended to provide an enormous amount of stability at speed) contribute to the reasons why steering results from weight shifts to the degree it does on a dirt bike.

No B.S.

At this writing, we have run nearly 100 riders of all experience levels on this double-barred bike. It has made believers out of every single one in the actuality of countersteering of course. Even at speeds of no more than 20 to 35 mph, no matter how much you tug or push or pull or jump around on the bike, the best we saw was that the bike wiggled and became somewhat unstable. Did it turn? Not really. Would it turn at higher speed? Absolutely not. Could you avoid something in your path? No Way. Could anyone quick turn the bike? Hopeless! The best result was one of my riding coaches. He got into a full hang-off position and was able to persuade the bike, by jerking on it, to start on a wide, wide arc in the paddock at Laguna Seca, a piece of asphalt that is about 500 X 800 feet. Like turning an oil tanker ship, start at noon and be on the turning arc at around 1:00 PM. It wasn't smooth and it wasn't very effective.We now call this bike "The NO BS Bike". There are no doubts in anyone's mind after they ride it that they have been countersteering all along. No doubts.You can hear riders who believed in the body steering method, laughing in their helmets at 100 yards away, once they get those solid-mounted bars in their hands and try to body steer the bike. They just shake their heads. No B.S.

For those who think you can steer by leaning without countersteering... Try riding a bike with locked up steering head bearings, my son recently bought a 1986 Yamaha FZ6 the steering head was almost completely locked in the center position. I took it down the sreet in front of my house and almost had ta lay er down! I think it's so subtle sometimes you don't even realize you're doing it.

I was at an off road down hill bicycle race last weekend, basically a motocross using gravity as the engine, these guys navigate deep ruts , loose rocks, roots off camber slopes, tight turns and jumps at speeds of 45 mph.

When they get kicked off line by any of the above, how do they know how and what kind of input to put into the bars?? They are looking where they want to GO, and practice, practice, practice fined tuned their REACTION (note I didn't say cognitive actions).

YES if you turn a single track vehicle you counter steer, but at some point you then turn into the turn, it magically happens, without thought and explanation and has been done for a little over a century and a half.

Has anybody figured out the geometry parameters that control the transition speed between
steering and counter steering and what affects the overlap between the two?

Even if you haven't figured it out it may be entertaining to hear some different theories.

That is something that anyone can find experimentally:

1) From total stop, balance the bike vertically, put both feet up on the pegs.
From that position, if you don't turn the handlebar, the bike will fall to either side.
Repeat and verify: the bike has no preferred side to fall onto.

2) From total stop, balance the bike vertically, put both feet up on the pegs.
From that position, turn handlebar all the way to the left (full lock), the bike will consistently fall to the left side.
Why?: You have moved the CG of the bike left and is now off the line that joins the contact patches of the front and rear tires.That is steering for you, and will work for standing still and for low speeds.
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1) From total stop, balance the bike vertically, put both feet up on the pegs.From that position, if you don't turn the handlebar, the bike will fall to either side.Repeat and verify: the bike has no preferred side to fall onto.

2) From total stop, balance the bike vertically, put both feet up on the pegs.From that position, turn handlebar all the way to the left (full lock), the bike will consistently fall to the left side.Why?: You have moved the CG of the bike left and is now off the line that joins the contact patches of the front and rear tires.That is steering for you, and will work for standing still and for low speeds.
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Your #2 is backwards. I think you're forgetting what the rake and trail are doing.

Seems to me there are a few people missing its point. Which is not to convince unbelievers that countersteering is fact, but to point out that learning to countersteer actively ie. to use what might seem like excessive countersteering to accentuate steering response is a useful thing to do. It gives the rider greater control, especially at higher speeds and when wanting to make rapid directional changes. True for me.

Don't believe in countersteering? Try the technique. You'll like what it does even if you don't accept the reasoning behind it.